Math 135 Winter 2015





Ebru Bekyel


Office hours: M 2:30–3:30, F 2:00-3:00 and Tu 1:30-2:30 in PDL-C 422. I am also in my office 9:30-10:20 every morning except Thursdays.


Teaching Assistant

Office Hours

Kolya Malkin

W 9:00-10:00, 5:00-6:00, S 4:00-5:00 in PDL-C 86


For the times and places of the sections see the schedule.



Calculus, 10th Edition, by Salas, Hille and Etgen, Chapters 11-14.

Ordinary Differential Equations, by Tenenbaum and Pollard, Chapters 4, 5, 6, and 11.


There will be two midterms, one final exam, homework assignments and quizzes. The midterms are 25% each, the final is 30%, the homework assignments are 10% and quizzes are 10% of your total grade. Late homework is not accepted and there are no quiz make ups. I will drop your lowest homework and quiz grade at the end of the quarter.

Week at a glance

Lectures are on MTuWF. Besides the textbooks, there will be supplementary handouts. I will not cover everything in lectures. You have to read the relevant sections in the textbooks and/or the handouts. Thursday quiz sections are for discussing problems with your TA. You should go to quiz sections prepared to ask and answer questions. There will be quizzes on most Thursdays. I will announce the quiz topic in lecture on Wednesdays if you remind me. The homework assignments are due on Mondays at the beginning of class.

Calculator policy

Calculators are not allowed on quizzes or exams.


Week of

Schedule and Announcements



·         From SHE: Sections 11.1-11.6
Cauchy Sequences
and Fixed Points by Tom Duchamp

·         You can follow your grades from

·         Homework #1, due Monday 01/12

·         Solutions to Homework #1



From SHE: Sections 11.7, 12.1-12.5 and approximating Infinite Series Using the Integral Test.

·         Homework #2, due Tuesday 01/20

·         Solutions to Homework #2


No class on 01/19

From SHE: Sections 12.6,12.7

·         Taylor Polynomials by Tom Duchamp

·         Homework #3, due Monday 01/26

·         Solutions to Homework #3



From SHE: Sections 12.8, 12.9, 10.2, 10.3

·         Complex Numbers The graph in the last part is wrong. Here is the correct version.

·         Homework #4 due Monday 02/02

·         Solutions to Homework #4

·         Here is a Midterm 1 Review and some hints.



Review. From TP: Picard Iteration, pages 719-734. Omit the proof of Theorem 58.5.

·         Midterm 1 on 02/03

·         Cauchy Sequences of Functions and Picard Iteration notes by Tom Duchamp.

·         Homework #5 due Monday 02/09

·         Solutions to Homework #5




From TP: Chapter 4 and Chapter 6 pages 313-326, 338-365.

·         Homework #6 due Tuesday 02/17

·         Solutions to Homework #6

·         Here is a practice sheet for the method of undetermined coefficients and the answers.

·         Here is a summary of Friday’s lecture including the link to the examples I talked about.


No class on 02/16


From TP: Chapter 5, pages 292-312

·         My lecture notes on the Laplace transform

·         We are not going to prove the injectivity of the Laplace transform in class. Here is a nice proof if you want to read it. The proof is not difficult, but it refers to another proof which is long.

·         A table of Laplace transforms. You will have this sheet in Midterm 2 and the Final Exam

·         Homework #7 due Monday 02/23

·         Solutions to Homework #7




·         Chapter 9, pages 531-546, from SHE Sections 13.1, 13.2.

·         Homework #8 due Monday 03/02

·         Here are some review problems for the second midterm.



Review,  From SHE: Sections 13.3-13.6

·         Midterm 2 on 03/03

·         Homework #9 due Monday 03/09

·         There are three ways we describe a line in space. There is an example on this page showing how to interpret them geometrically. Note that I used <a,b,c> for vectors instead of (a,b,c).




From SHE: Sections 14.1-14.5

·         Homework #10 due FRIDAY the 13th

·         Here is a nice animation of the Frenet frame (also called the TNB frame) of Project 14.5B.

·         Here are animations showing how a vector function traces a curve in space and the definition of the derivative as a limit.

·         These animations show the osculating and normal planes of a curve.

·         Here is a final exam review and hints for the solutions. On the final exam, I am planning to ask two questions from each of the three parts: sequences and series, DEs, vector calculus.


Final Exam

Monday, March 16, 2015,8:30-10:20, BNS 203